What are the most important client-side (HTML5/CSS/JavaScript) libraries and why?

All of these technologies which are mentioned (i.e. HTML5, CSS and Javascript) are important.

Please note that CSS is for styling the different elements of DOM.

HTML5 is latest version of HTML having new features such as localstorage, media tags, specific tags such as <section>, articles, <nav> etc.

And Javascript is a must when you are working on client side.

You can avoid HTML5 and can use simple HTML , but for styling you have to use CSS and for interaction with the services, for manipulating different conditions etc Javascript is must. That is why these are very important.